Of the vast number of algorithms used in modem computer image generation, most rely upon data bases comprised of polygons. This constraint on the image generation system becomes a severe impediment when curved objects must be modeled and displayed with an acceptable level of speed and accuracy. A technique is needed which provides a means of modeling curved surfaces, storing them in a data base, and displaying them using existing algorithms.

Tessellation is one method of achieving such goals. A curved object is represented by some characteristic geometry of the object's surface, such as points and tangent vectors. A set of equations is extrapolated from this geometry and evaluated at discrete points across the surface. These points are then combined to form a polygon mesh which approximates the original curved surf ace.

Tessellation provides advantages over conventional methods of curved surface display in terms of modeling and data base generation, scene realism, and system throughput. An object modeled with characteristic geometry is easily modified and results in a more compressed data base. In addition, any characteristic geometry may be sampled in different ways to yield many levels of detail. This improves realism and speed, as distant objects would generate fewer polygons than would an object in the foreground.

This report shall analyze the theory of tessellation and demonstrate the capabilities of the algorithms presented. The advantages and disadvantages of tessellation in computer image generation will also be examined.


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